Properties

Label 320.3.h.f.319.5
Level $320$
Weight $3$
Character 320.319
Analytic conductor $8.719$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 320.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.71936845953\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.1827904.1
Defining polynomial: \(x^{6} + 9 x^{4} + 14 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 319.5
Root \(-2.65109i\) of defining polynomial
Character \(\chi\) \(=\) 320.319
Dual form 320.3.h.f.319.6

$q$-expansion

\(f(q)\) \(=\) \(q+2.75441 q^{3} +(-4.30219 - 2.54778i) q^{5} -3.84997 q^{7} -1.41325 q^{9} +O(q^{10})\) \(q+2.75441 q^{3} +(-4.30219 - 2.54778i) q^{5} -3.84997 q^{7} -1.41325 q^{9} -6.19112i q^{11} -16.1132i q^{13} +(-11.8500 - 7.01762i) q^{15} +5.20875i q^{17} -36.2264i q^{19} -10.6044 q^{21} -22.0411 q^{23} +(12.0176 + 21.9221i) q^{25} -28.6823 q^{27} +20.0352 q^{29} -26.4175i q^{31} -17.0529i q^{33} +(16.5633 + 9.80888i) q^{35} +69.3219i q^{37} -44.3822i q^{39} +11.6220 q^{41} -25.8542 q^{43} +(6.08006 + 3.60065i) q^{45} +66.1853 q^{47} -34.1777 q^{49} +14.3470i q^{51} -39.5751i q^{53} +(-15.7736 + 26.6354i) q^{55} -99.7821i q^{57} -27.7736i q^{59} +54.1954 q^{61} +5.44096 q^{63} +(-41.0529 + 69.3219i) q^{65} -107.507 q^{67} -60.7101 q^{69} +70.7997i q^{71} -37.4351i q^{73} +(33.1014 + 60.3822i) q^{75} +23.8356i q^{77} -97.6530i q^{79} -66.2835 q^{81} +126.163 q^{83} +(13.2707 - 22.4090i) q^{85} +55.1852 q^{87} +133.635 q^{89} +62.0352i q^{91} -72.7645i q^{93} +(-92.2969 + 155.853i) q^{95} -6.40900i q^{97} +8.74960i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{3} + 2 q^{5} + 12 q^{7} + 18 q^{9} + O(q^{10}) \) \( 6 q - 4 q^{3} + 2 q^{5} + 12 q^{7} + 18 q^{9} - 36 q^{15} - 8 q^{21} - 68 q^{23} - 10 q^{25} - 184 q^{27} - 44 q^{29} + 108 q^{35} - 68 q^{41} + 76 q^{43} + 6 q^{45} + 268 q^{47} - 62 q^{49} - 288 q^{55} + 100 q^{61} - 172 q^{63} - 308 q^{67} + 184 q^{69} + 284 q^{75} + 238 q^{81} + 204 q^{83} + 32 q^{85} + 584 q^{87} + 76 q^{89} - 32 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.75441 0.918135 0.459068 0.888401i \(-0.348184\pi\)
0.459068 + 0.888401i \(0.348184\pi\)
\(4\) 0 0
\(5\) −4.30219 2.54778i −0.860437 0.509556i
\(6\) 0 0
\(7\) −3.84997 −0.549995 −0.274998 0.961445i \(-0.588677\pi\)
−0.274998 + 0.961445i \(0.588677\pi\)
\(8\) 0 0
\(9\) −1.41325 −0.157028
\(10\) 0 0
\(11\) 6.19112i 0.562829i −0.959586 0.281415i \(-0.909196\pi\)
0.959586 0.281415i \(-0.0908037\pi\)
\(12\) 0 0
\(13\) 16.1132i 1.23948i −0.784809 0.619738i \(-0.787239\pi\)
0.784809 0.619738i \(-0.212761\pi\)
\(14\) 0 0
\(15\) −11.8500 7.01762i −0.789998 0.467842i
\(16\) 0 0
\(17\) 5.20875i 0.306397i 0.988195 + 0.153198i \(0.0489574\pi\)
−0.988195 + 0.153198i \(0.951043\pi\)
\(18\) 0 0
\(19\) 36.2264i 1.90665i −0.301944 0.953326i \(-0.597636\pi\)
0.301944 0.953326i \(-0.402364\pi\)
\(20\) 0 0
\(21\) −10.6044 −0.504970
\(22\) 0 0
\(23\) −22.0411 −0.958308 −0.479154 0.877731i \(-0.659057\pi\)
−0.479154 + 0.877731i \(0.659057\pi\)
\(24\) 0 0
\(25\) 12.0176 + 21.9221i 0.480705 + 0.876882i
\(26\) 0 0
\(27\) −28.6823 −1.06231
\(28\) 0 0
\(29\) 20.0352 0.690871 0.345435 0.938443i \(-0.387731\pi\)
0.345435 + 0.938443i \(0.387731\pi\)
\(30\) 0 0
\(31\) 26.4175i 0.852177i −0.904681 0.426089i \(-0.859891\pi\)
0.904681 0.426089i \(-0.140109\pi\)
\(32\) 0 0
\(33\) 17.0529i 0.516754i
\(34\) 0 0
\(35\) 16.5633 + 9.80888i 0.473237 + 0.280254i
\(36\) 0 0
\(37\) 69.3219i 1.87357i 0.349911 + 0.936783i \(0.386212\pi\)
−0.349911 + 0.936783i \(0.613788\pi\)
\(38\) 0 0
\(39\) 44.3822i 1.13801i
\(40\) 0 0
\(41\) 11.6220 0.283463 0.141732 0.989905i \(-0.454733\pi\)
0.141732 + 0.989905i \(0.454733\pi\)
\(42\) 0 0
\(43\) −25.8542 −0.601261 −0.300630 0.953741i \(-0.597197\pi\)
−0.300630 + 0.953741i \(0.597197\pi\)
\(44\) 0 0
\(45\) 6.08006 + 3.60065i 0.135112 + 0.0800144i
\(46\) 0 0
\(47\) 66.1853 1.40820 0.704099 0.710102i \(-0.251351\pi\)
0.704099 + 0.710102i \(0.251351\pi\)
\(48\) 0 0
\(49\) −34.1777 −0.697505
\(50\) 0 0
\(51\) 14.3470i 0.281314i
\(52\) 0 0
\(53\) 39.5751i 0.746699i −0.927691 0.373350i \(-0.878209\pi\)
0.927691 0.373350i \(-0.121791\pi\)
\(54\) 0 0
\(55\) −15.7736 + 26.6354i −0.286793 + 0.484280i
\(56\) 0 0
\(57\) 99.7821i 1.75056i
\(58\) 0 0
\(59\) 27.7736i 0.470739i −0.971906 0.235370i \(-0.924370\pi\)
0.971906 0.235370i \(-0.0756301\pi\)
\(60\) 0 0
\(61\) 54.1954 0.888449 0.444224 0.895916i \(-0.353479\pi\)
0.444224 + 0.895916i \(0.353479\pi\)
\(62\) 0 0
\(63\) 5.44096 0.0863645
\(64\) 0 0
\(65\) −41.0529 + 69.3219i −0.631583 + 1.06649i
\(66\) 0 0
\(67\) −107.507 −1.60459 −0.802293 0.596931i \(-0.796387\pi\)
−0.802293 + 0.596931i \(0.796387\pi\)
\(68\) 0 0
\(69\) −60.7101 −0.879857
\(70\) 0 0
\(71\) 70.7997i 0.997179i 0.866838 + 0.498590i \(0.166149\pi\)
−0.866838 + 0.498590i \(0.833851\pi\)
\(72\) 0 0
\(73\) 37.4351i 0.512810i −0.966569 0.256405i \(-0.917462\pi\)
0.966569 0.256405i \(-0.0825380\pi\)
\(74\) 0 0
\(75\) 33.1014 + 60.3822i 0.441352 + 0.805097i
\(76\) 0 0
\(77\) 23.8356i 0.309554i
\(78\) 0 0
\(79\) 97.6530i 1.23611i −0.786133 0.618057i \(-0.787920\pi\)
0.786133 0.618057i \(-0.212080\pi\)
\(80\) 0 0
\(81\) −66.2835 −0.818315
\(82\) 0 0
\(83\) 126.163 1.52003 0.760017 0.649904i \(-0.225191\pi\)
0.760017 + 0.649904i \(0.225191\pi\)
\(84\) 0 0
\(85\) 13.2707 22.4090i 0.156126 0.263635i
\(86\) 0 0
\(87\) 55.1852 0.634313
\(88\) 0 0
\(89\) 133.635 1.50151 0.750757 0.660579i \(-0.229689\pi\)
0.750757 + 0.660579i \(0.229689\pi\)
\(90\) 0 0
\(91\) 62.0352i 0.681706i
\(92\) 0 0
\(93\) 72.7645i 0.782414i
\(94\) 0 0
\(95\) −92.2969 + 155.853i −0.971546 + 1.64055i
\(96\) 0 0
\(97\) 6.40900i 0.0660722i −0.999454 0.0330361i \(-0.989482\pi\)
0.999454 0.0330361i \(-0.0105176\pi\)
\(98\) 0 0
\(99\) 8.74960i 0.0883798i
\(100\) 0 0
\(101\) −121.564 −1.20361 −0.601803 0.798644i \(-0.705551\pi\)
−0.601803 + 0.798644i \(0.705551\pi\)
\(102\) 0 0
\(103\) 9.95891 0.0966884 0.0483442 0.998831i \(-0.484606\pi\)
0.0483442 + 0.998831i \(0.484606\pi\)
\(104\) 0 0
\(105\) 45.6220 + 27.0176i 0.434495 + 0.257311i
\(106\) 0 0
\(107\) 134.842 1.26020 0.630102 0.776512i \(-0.283013\pi\)
0.630102 + 0.776512i \(0.283013\pi\)
\(108\) 0 0
\(109\) 28.2306 0.258996 0.129498 0.991580i \(-0.458663\pi\)
0.129498 + 0.991580i \(0.458663\pi\)
\(110\) 0 0
\(111\) 190.941i 1.72019i
\(112\) 0 0
\(113\) 190.052i 1.68188i 0.541130 + 0.840939i \(0.317997\pi\)
−0.541130 + 0.840939i \(0.682003\pi\)
\(114\) 0 0
\(115\) 94.8249 + 56.1559i 0.824564 + 0.488312i
\(116\) 0 0
\(117\) 22.7719i 0.194632i
\(118\) 0 0
\(119\) 20.0535i 0.168517i
\(120\) 0 0
\(121\) 82.6700 0.683223
\(122\) 0 0
\(123\) 32.0117 0.260258
\(124\) 0 0
\(125\) 4.15055 124.931i 0.0332044 0.999449i
\(126\) 0 0
\(127\) 60.0646 0.472950 0.236475 0.971638i \(-0.424008\pi\)
0.236475 + 0.971638i \(0.424008\pi\)
\(128\) 0 0
\(129\) −71.2130 −0.552039
\(130\) 0 0
\(131\) 111.985i 0.854848i 0.904051 + 0.427424i \(0.140579\pi\)
−0.904051 + 0.427424i \(0.859421\pi\)
\(132\) 0 0
\(133\) 139.470i 1.04865i
\(134\) 0 0
\(135\) 123.397 + 73.0763i 0.914049 + 0.541306i
\(136\) 0 0
\(137\) 42.6439i 0.311269i 0.987815 + 0.155635i \(0.0497422\pi\)
−0.987815 + 0.155635i \(0.950258\pi\)
\(138\) 0 0
\(139\) 222.332i 1.59951i −0.600325 0.799756i \(-0.704962\pi\)
0.600325 0.799756i \(-0.295038\pi\)
\(140\) 0 0
\(141\) 182.301 1.29292
\(142\) 0 0
\(143\) −99.7587 −0.697614
\(144\) 0 0
\(145\) −86.1954 51.0454i −0.594451 0.352037i
\(146\) 0 0
\(147\) −94.1394 −0.640404
\(148\) 0 0
\(149\) −20.0981 −0.134887 −0.0674434 0.997723i \(-0.521484\pi\)
−0.0674434 + 0.997723i \(0.521484\pi\)
\(150\) 0 0
\(151\) 86.0522i 0.569882i −0.958545 0.284941i \(-0.908026\pi\)
0.958545 0.284941i \(-0.0919741\pi\)
\(152\) 0 0
\(153\) 7.36126i 0.0481128i
\(154\) 0 0
\(155\) −67.3060 + 113.653i −0.434232 + 0.733245i
\(156\) 0 0
\(157\) 16.0342i 0.102129i −0.998695 0.0510643i \(-0.983739\pi\)
0.998695 0.0510643i \(-0.0162614\pi\)
\(158\) 0 0
\(159\) 109.006i 0.685571i
\(160\) 0 0
\(161\) 84.8575 0.527065
\(162\) 0 0
\(163\) −179.157 −1.09912 −0.549561 0.835454i \(-0.685205\pi\)
−0.549561 + 0.835454i \(0.685205\pi\)
\(164\) 0 0
\(165\) −43.4470 + 73.3646i −0.263315 + 0.444634i
\(166\) 0 0
\(167\) −137.800 −0.825149 −0.412574 0.910924i \(-0.635370\pi\)
−0.412574 + 0.910924i \(0.635370\pi\)
\(168\) 0 0
\(169\) −90.6347 −0.536300
\(170\) 0 0
\(171\) 51.1969i 0.299397i
\(172\) 0 0
\(173\) 62.8895i 0.363523i 0.983343 + 0.181762i \(0.0581799\pi\)
−0.983343 + 0.181762i \(0.941820\pi\)
\(174\) 0 0
\(175\) −46.2675 84.3992i −0.264385 0.482281i
\(176\) 0 0
\(177\) 76.4998i 0.432203i
\(178\) 0 0
\(179\) 238.020i 1.32972i −0.746967 0.664861i \(-0.768491\pi\)
0.746967 0.664861i \(-0.231509\pi\)
\(180\) 0 0
\(181\) −186.718 −1.03159 −0.515795 0.856712i \(-0.672503\pi\)
−0.515795 + 0.856712i \(0.672503\pi\)
\(182\) 0 0
\(183\) 149.276 0.815716
\(184\) 0 0
\(185\) 176.617 298.236i 0.954687 1.61209i
\(186\) 0 0
\(187\) 32.2480 0.172449
\(188\) 0 0
\(189\) 110.426 0.584264
\(190\) 0 0
\(191\) 123.447i 0.646319i −0.946344 0.323160i \(-0.895255\pi\)
0.946344 0.323160i \(-0.104745\pi\)
\(192\) 0 0
\(193\) 162.355i 0.841220i −0.907242 0.420610i \(-0.861816\pi\)
0.907242 0.420610i \(-0.138184\pi\)
\(194\) 0 0
\(195\) −113.076 + 190.941i −0.579878 + 0.979183i
\(196\) 0 0
\(197\) 113.540i 0.576344i −0.957579 0.288172i \(-0.906952\pi\)
0.957579 0.288172i \(-0.0930475\pi\)
\(198\) 0 0
\(199\) 325.928i 1.63783i −0.573915 0.818915i \(-0.694576\pi\)
0.573915 0.818915i \(-0.305424\pi\)
\(200\) 0 0
\(201\) −296.118 −1.47323
\(202\) 0 0
\(203\) −77.1351 −0.379976
\(204\) 0 0
\(205\) −50.0000 29.6103i −0.243902 0.144441i
\(206\) 0 0
\(207\) 31.1496 0.150481
\(208\) 0 0
\(209\) −224.282 −1.07312
\(210\) 0 0
\(211\) 130.731i 0.619580i −0.950805 0.309790i \(-0.899741\pi\)
0.950805 0.309790i \(-0.100259\pi\)
\(212\) 0 0
\(213\) 195.011i 0.915546i
\(214\) 0 0
\(215\) 111.230 + 65.8709i 0.517347 + 0.306376i
\(216\) 0 0
\(217\) 101.707i 0.468694i
\(218\) 0 0
\(219\) 103.112i 0.470829i
\(220\) 0 0
\(221\) 83.9295 0.379772
\(222\) 0 0
\(223\) 93.3889 0.418784 0.209392 0.977832i \(-0.432851\pi\)
0.209392 + 0.977832i \(0.432851\pi\)
\(224\) 0 0
\(225\) −16.9839 30.9813i −0.0754840 0.137695i
\(226\) 0 0
\(227\) 14.9957 0.0660602 0.0330301 0.999454i \(-0.489484\pi\)
0.0330301 + 0.999454i \(0.489484\pi\)
\(228\) 0 0
\(229\) 144.106 0.629283 0.314641 0.949211i \(-0.398116\pi\)
0.314641 + 0.949211i \(0.398116\pi\)
\(230\) 0 0
\(231\) 65.6530i 0.284212i
\(232\) 0 0
\(233\) 126.528i 0.543040i 0.962433 + 0.271520i \(0.0875263\pi\)
−0.962433 + 0.271520i \(0.912474\pi\)
\(234\) 0 0
\(235\) −284.741 168.626i −1.21167 0.717556i
\(236\) 0 0
\(237\) 268.976i 1.13492i
\(238\) 0 0
\(239\) 1.65300i 0.00691630i −0.999994 0.00345815i \(-0.998899\pi\)
0.999994 0.00345815i \(-0.00110077\pi\)
\(240\) 0 0
\(241\) 206.928 0.858622 0.429311 0.903157i \(-0.358756\pi\)
0.429311 + 0.903157i \(0.358756\pi\)
\(242\) 0 0
\(243\) 75.5692 0.310984
\(244\) 0 0
\(245\) 147.039 + 87.0774i 0.600159 + 0.355418i
\(246\) 0 0
\(247\) −583.722 −2.36325
\(248\) 0 0
\(249\) 347.503 1.39560
\(250\) 0 0
\(251\) 74.1206i 0.295301i −0.989040 0.147651i \(-0.952829\pi\)
0.989040 0.147651i \(-0.0471711\pi\)
\(252\) 0 0
\(253\) 136.459i 0.539364i
\(254\) 0 0
\(255\) 36.5530 61.7235i 0.143345 0.242053i
\(256\) 0 0
\(257\) 274.682i 1.06880i 0.845231 + 0.534402i \(0.179463\pi\)
−0.845231 + 0.534402i \(0.820537\pi\)
\(258\) 0 0
\(259\) 266.887i 1.03045i
\(260\) 0 0
\(261\) −28.3148 −0.108486
\(262\) 0 0
\(263\) −75.5382 −0.287218 −0.143609 0.989635i \(-0.545871\pi\)
−0.143609 + 0.989635i \(0.545871\pi\)
\(264\) 0 0
\(265\) −100.829 + 170.259i −0.380485 + 0.642488i
\(266\) 0 0
\(267\) 368.084 1.37859
\(268\) 0 0
\(269\) −314.087 −1.16761 −0.583804 0.811895i \(-0.698436\pi\)
−0.583804 + 0.811895i \(0.698436\pi\)
\(270\) 0 0
\(271\) 128.158i 0.472908i −0.971643 0.236454i \(-0.924015\pi\)
0.971643 0.236454i \(-0.0759852\pi\)
\(272\) 0 0
\(273\) 170.870i 0.625898i
\(274\) 0 0
\(275\) 135.722 74.4026i 0.493535 0.270555i
\(276\) 0 0
\(277\) 242.118i 0.874073i −0.899444 0.437037i \(-0.856028\pi\)
0.899444 0.437037i \(-0.143972\pi\)
\(278\) 0 0
\(279\) 37.3345i 0.133815i
\(280\) 0 0
\(281\) 28.8562 0.102691 0.0513456 0.998681i \(-0.483649\pi\)
0.0513456 + 0.998681i \(0.483649\pi\)
\(282\) 0 0
\(283\) −269.993 −0.954039 −0.477020 0.878893i \(-0.658283\pi\)
−0.477020 + 0.878893i \(0.658283\pi\)
\(284\) 0 0
\(285\) −254.223 + 429.281i −0.892011 + 1.50625i
\(286\) 0 0
\(287\) −44.7443 −0.155904
\(288\) 0 0
\(289\) 261.869 0.906121
\(290\) 0 0
\(291\) 17.6530i 0.0606632i
\(292\) 0 0
\(293\) 353.448i 1.20631i −0.797625 0.603154i \(-0.793911\pi\)
0.797625 0.603154i \(-0.206089\pi\)
\(294\) 0 0
\(295\) −70.7611 + 119.487i −0.239868 + 0.405042i
\(296\) 0 0
\(297\) 177.576i 0.597898i
\(298\) 0 0
\(299\) 355.152i 1.18780i
\(300\) 0 0
\(301\) 99.5379 0.330691
\(302\) 0 0
\(303\) −334.837 −1.10507
\(304\) 0 0
\(305\) −233.159 138.078i −0.764454 0.452715i
\(306\) 0 0
\(307\) 260.946 0.849985 0.424993 0.905197i \(-0.360277\pi\)
0.424993 + 0.905197i \(0.360277\pi\)
\(308\) 0 0
\(309\) 27.4309 0.0887730
\(310\) 0 0
\(311\) 141.570i 0.455208i 0.973754 + 0.227604i \(0.0730892\pi\)
−0.973754 + 0.227604i \(0.926911\pi\)
\(312\) 0 0
\(313\) 365.950i 1.16917i −0.811333 0.584584i \(-0.801258\pi\)
0.811333 0.584584i \(-0.198742\pi\)
\(314\) 0 0
\(315\) −23.4080 13.8624i −0.0743113 0.0440076i
\(316\) 0 0
\(317\) 9.22805i 0.0291106i 0.999894 + 0.0145553i \(0.00463326\pi\)
−0.999894 + 0.0145553i \(0.995367\pi\)
\(318\) 0 0
\(319\) 124.041i 0.388842i
\(320\) 0 0
\(321\) 371.409 1.15704
\(322\) 0 0
\(323\) 188.694 0.584192
\(324\) 0 0
\(325\) 353.234 193.642i 1.08687 0.595822i
\(326\) 0 0
\(327\) 77.7586 0.237794
\(328\) 0 0
\(329\) −254.811 −0.774502
\(330\) 0 0
\(331\) 53.3799i 0.161268i 0.996744 + 0.0806342i \(0.0256946\pi\)
−0.996744 + 0.0806342i \(0.974305\pi\)
\(332\) 0 0
\(333\) 97.9692i 0.294202i
\(334\) 0 0
\(335\) 462.516 + 273.905i 1.38065 + 0.817626i
\(336\) 0 0
\(337\) 350.458i 1.03994i 0.854186 + 0.519968i \(0.174056\pi\)
−0.854186 + 0.519968i \(0.825944\pi\)
\(338\) 0 0
\(339\) 523.481i 1.54419i
\(340\) 0 0
\(341\) −163.554 −0.479630
\(342\) 0 0
\(343\) 320.232 0.933620
\(344\) 0 0
\(345\) 261.186 + 154.676i 0.757062 + 0.448336i
\(346\) 0 0
\(347\) −70.8302 −0.204122 −0.102061 0.994778i \(-0.532544\pi\)
−0.102061 + 0.994778i \(0.532544\pi\)
\(348\) 0 0
\(349\) −373.045 −1.06890 −0.534449 0.845201i \(-0.679481\pi\)
−0.534449 + 0.845201i \(0.679481\pi\)
\(350\) 0 0
\(351\) 462.163i 1.31670i
\(352\) 0 0
\(353\) 543.568i 1.53985i −0.638132 0.769927i \(-0.720293\pi\)
0.638132 0.769927i \(-0.279707\pi\)
\(354\) 0 0
\(355\) 180.382 304.594i 0.508119 0.858010i
\(356\) 0 0
\(357\) 55.2355i 0.154721i
\(358\) 0 0
\(359\) 500.805i 1.39500i 0.716585 + 0.697500i \(0.245704\pi\)
−0.716585 + 0.697500i \(0.754296\pi\)
\(360\) 0 0
\(361\) −951.350 −2.63532
\(362\) 0 0
\(363\) 227.707 0.627291
\(364\) 0 0
\(365\) −95.3765 + 161.053i −0.261305 + 0.441241i
\(366\) 0 0
\(367\) 142.499 0.388281 0.194140 0.980974i \(-0.437808\pi\)
0.194140 + 0.980974i \(0.437808\pi\)
\(368\) 0 0
\(369\) −16.4248 −0.0445116
\(370\) 0 0
\(371\) 152.363i 0.410681i
\(372\) 0 0
\(373\) 160.000i 0.428954i −0.976729 0.214477i \(-0.931195\pi\)
0.976729 0.214477i \(-0.0688047\pi\)
\(374\) 0 0
\(375\) 11.4323 344.111i 0.0304862 0.917629i
\(376\) 0 0
\(377\) 322.832i 0.856317i
\(378\) 0 0
\(379\) 192.796i 0.508698i 0.967113 + 0.254349i \(0.0818611\pi\)
−0.967113 + 0.254349i \(0.918139\pi\)
\(380\) 0 0
\(381\) 165.442 0.434232
\(382\) 0 0
\(383\) 605.286 1.58038 0.790191 0.612861i \(-0.209981\pi\)
0.790191 + 0.612861i \(0.209981\pi\)
\(384\) 0 0
\(385\) 60.7280 102.545i 0.157735 0.266352i
\(386\) 0 0
\(387\) 36.5384 0.0944146
\(388\) 0 0
\(389\) 522.159 1.34231 0.671155 0.741317i \(-0.265798\pi\)
0.671155 + 0.741317i \(0.265798\pi\)
\(390\) 0 0
\(391\) 114.806i 0.293623i
\(392\) 0 0
\(393\) 308.452i 0.784866i
\(394\) 0 0
\(395\) −248.798 + 420.121i −0.629870 + 1.06360i
\(396\) 0 0
\(397\) 357.537i 0.900598i 0.892878 + 0.450299i \(0.148683\pi\)
−0.892878 + 0.450299i \(0.851317\pi\)
\(398\) 0 0
\(399\) 384.158i 0.962802i
\(400\) 0 0
\(401\) 262.506 0.654629 0.327315 0.944915i \(-0.393856\pi\)
0.327315 + 0.944915i \(0.393856\pi\)
\(402\) 0 0
\(403\) −425.670 −1.05625
\(404\) 0 0
\(405\) 285.164 + 168.876i 0.704108 + 0.416977i
\(406\) 0 0
\(407\) 429.181 1.05450
\(408\) 0 0
\(409\) −63.2015 −0.154527 −0.0772634 0.997011i \(-0.524618\pi\)
−0.0772634 + 0.997011i \(0.524618\pi\)
\(410\) 0 0
\(411\) 117.459i 0.285787i
\(412\) 0 0
\(413\) 106.928i 0.258905i
\(414\) 0 0
\(415\) −542.776 321.435i −1.30789 0.774542i
\(416\) 0 0
\(417\) 612.393i 1.46857i
\(418\) 0 0
\(419\) 673.390i 1.60714i 0.595213 + 0.803568i \(0.297068\pi\)
−0.595213 + 0.803568i \(0.702932\pi\)
\(420\) 0 0
\(421\) −84.6877 −0.201158 −0.100579 0.994929i \(-0.532070\pi\)
−0.100579 + 0.994929i \(0.532070\pi\)
\(422\) 0 0
\(423\) −93.5363 −0.221126
\(424\) 0 0
\(425\) −114.186 + 62.5968i −0.268674 + 0.147286i
\(426\) 0 0
\(427\) −208.650 −0.488643
\(428\) 0 0
\(429\) −274.776 −0.640504
\(430\) 0 0
\(431\) 672.158i 1.55953i −0.626072 0.779766i \(-0.715338\pi\)
0.626072 0.779766i \(-0.284662\pi\)
\(432\) 0 0
\(433\) 562.185i 1.29835i −0.760640 0.649174i \(-0.775115\pi\)
0.760640 0.649174i \(-0.224885\pi\)
\(434\) 0 0
\(435\) −237.417 140.600i −0.545786 0.323218i
\(436\) 0 0
\(437\) 798.469i 1.82716i
\(438\) 0 0
\(439\) 384.842i 0.876633i 0.898821 + 0.438316i \(0.144425\pi\)
−0.898821 + 0.438316i \(0.855575\pi\)
\(440\) 0 0
\(441\) 48.3017 0.109528
\(442\) 0 0
\(443\) 461.625 1.04204 0.521021 0.853544i \(-0.325551\pi\)
0.521021 + 0.853544i \(0.325551\pi\)
\(444\) 0 0
\(445\) −574.922 340.472i −1.29196 0.765106i
\(446\) 0 0
\(447\) −55.3584 −0.123844
\(448\) 0 0
\(449\) 48.7390 0.108550 0.0542750 0.998526i \(-0.482715\pi\)
0.0542750 + 0.998526i \(0.482715\pi\)
\(450\) 0 0
\(451\) 71.9532i 0.159542i
\(452\) 0 0
\(453\) 237.023i 0.523229i
\(454\) 0 0
\(455\) 158.052 266.887i 0.347368 0.586565i
\(456\) 0 0
\(457\) 762.588i 1.66868i 0.551248 + 0.834341i \(0.314152\pi\)
−0.551248 + 0.834341i \(0.685848\pi\)
\(458\) 0 0
\(459\) 149.399i 0.325488i
\(460\) 0 0
\(461\) 406.436 0.881639 0.440820 0.897596i \(-0.354688\pi\)
0.440820 + 0.897596i \(0.354688\pi\)
\(462\) 0 0
\(463\) −260.743 −0.563159 −0.281580 0.959538i \(-0.590858\pi\)
−0.281580 + 0.959538i \(0.590858\pi\)
\(464\) 0 0
\(465\) −185.388 + 313.046i −0.398684 + 0.673218i
\(466\) 0 0
\(467\) −594.738 −1.27353 −0.636765 0.771058i \(-0.719728\pi\)
−0.636765 + 0.771058i \(0.719728\pi\)
\(468\) 0 0
\(469\) 413.899 0.882515
\(470\) 0 0
\(471\) 44.1647i 0.0937679i
\(472\) 0 0
\(473\) 160.067i 0.338407i
\(474\) 0 0
\(475\) 794.157 435.355i 1.67191 0.916537i
\(476\) 0 0
\(477\) 55.9294i 0.117252i
\(478\) 0 0
\(479\) 534.894i 1.11669i 0.829609 + 0.558344i \(0.188563\pi\)
−0.829609 + 0.558344i \(0.811437\pi\)
\(480\) 0 0
\(481\) 1117.00 2.32224
\(482\) 0 0
\(483\) 233.732 0.483917
\(484\) 0 0
\(485\) −16.3287 + 27.5727i −0.0336675 + 0.0568510i
\(486\) 0 0
\(487\) 264.298 0.542706 0.271353 0.962480i \(-0.412529\pi\)
0.271353 + 0.962480i \(0.412529\pi\)
\(488\) 0 0
\(489\) −493.471 −1.00914
\(490\) 0 0
\(491\) 539.150i 1.09807i −0.835801 0.549033i \(-0.814996\pi\)
0.835801 0.549033i \(-0.185004\pi\)
\(492\) 0 0
\(493\) 104.359i 0.211681i
\(494\) 0 0
\(495\) 22.2921 37.6424i 0.0450345 0.0760453i
\(496\) 0 0
\(497\) 272.577i 0.548444i
\(498\) 0 0
\(499\) 138.218i 0.276991i −0.990363 0.138495i \(-0.955773\pi\)
0.990363 0.138495i \(-0.0442266\pi\)
\(500\) 0 0
\(501\) −379.557 −0.757598
\(502\) 0 0
\(503\) −389.170 −0.773697 −0.386848 0.922143i \(-0.626436\pi\)
−0.386848 + 0.922143i \(0.626436\pi\)
\(504\) 0 0
\(505\) 522.992 + 309.719i 1.03563 + 0.613305i
\(506\) 0 0
\(507\) −249.645 −0.492396
\(508\) 0 0
\(509\) 468.599 0.920627 0.460314 0.887756i \(-0.347737\pi\)
0.460314 + 0.887756i \(0.347737\pi\)
\(510\) 0 0
\(511\) 144.124i 0.282043i
\(512\) 0 0
\(513\) 1039.06i 2.02545i
\(514\) 0 0
\(515\) −42.8451 25.3731i −0.0831943 0.0492682i
\(516\) 0 0
\(517\) 409.761i 0.792575i
\(518\) 0 0
\(519\) 173.223i 0.333764i
\(520\) 0 0
\(521\) −931.151 −1.78724 −0.893619 0.448826i \(-0.851842\pi\)
−0.893619 + 0.448826i \(0.851842\pi\)
\(522\) 0 0
\(523\) −227.656 −0.435289 −0.217645 0.976028i \(-0.569837\pi\)
−0.217645 + 0.976028i \(0.569837\pi\)
\(524\) 0 0
\(525\) −127.439 232.470i −0.242742 0.442799i
\(526\) 0 0
\(527\) 137.602 0.261104
\(528\) 0 0
\(529\) −43.1902 −0.0816451
\(530\) 0 0
\(531\) 39.2511i 0.0739191i
\(532\) 0 0
\(533\) 187.267i 0.351346i
\(534\) 0 0
\(535\) −580.115 343.548i −1.08433 0.642145i
\(536\) 0 0
\(537\) 655.605i 1.22087i
\(538\) 0 0
\(539\) 211.599i 0.392576i
\(540\) 0 0
\(541\) −388.174 −0.717511 −0.358756 0.933431i \(-0.616799\pi\)
−0.358756 + 0.933431i \(0.616799\pi\)
\(542\) 0 0
\(543\) −514.296 −0.947139
\(544\) 0 0
\(545\) −121.453 71.9254i −0.222850 0.131973i
\(546\) 0 0
\(547\) 473.059 0.864824 0.432412 0.901676i \(-0.357663\pi\)
0.432412 + 0.901676i \(0.357663\pi\)
\(548\) 0 0
\(549\) −76.5916 −0.139511
\(550\) 0 0
\(551\) 725.804i 1.31725i
\(552\) 0 0
\(553\) 375.961i 0.679857i
\(554\) 0 0
\(555\) 486.475 821.463i 0.876532 1.48011i
\(556\) 0 0
\(557\) 419.101i 0.752426i 0.926533 + 0.376213i \(0.122774\pi\)
−0.926533 + 0.376213i \(0.877226\pi\)
\(558\) 0 0
\(559\) 416.594i 0.745248i
\(560\) 0 0
\(561\) 88.8241 0.158332
\(562\) 0 0
\(563\) −145.910 −0.259165 −0.129582 0.991569i \(-0.541364\pi\)
−0.129582 + 0.991569i \(0.541364\pi\)
\(564\) 0 0
\(565\) 484.211 817.640i 0.857011 1.44715i
\(566\) 0 0
\(567\) 255.189 0.450069
\(568\) 0 0
\(569\) 950.513 1.67050 0.835249 0.549872i \(-0.185323\pi\)
0.835249 + 0.549872i \(0.185323\pi\)
\(570\) 0 0
\(571\) 404.107i 0.707717i −0.935299 0.353859i \(-0.884869\pi\)
0.935299 0.353859i \(-0.115131\pi\)
\(572\) 0 0
\(573\) 340.023i 0.593408i
\(574\) 0 0
\(575\) −264.882 483.186i −0.460664 0.840324i
\(576\) 0 0
\(577\) 847.944i 1.46957i −0.678298 0.734787i \(-0.737282\pi\)
0.678298 0.734787i \(-0.262718\pi\)
\(578\) 0 0
\(579\) 447.193i 0.772354i
\(580\) 0 0
\(581\) −485.723 −0.836011
\(582\) 0 0
\(583\) −245.014 −0.420264
\(584\) 0 0
\(585\) 58.0179 97.9692i 0.0991760 0.167469i
\(586\) 0 0
\(587\) −658.243 −1.12137 −0.560684 0.828030i \(-0.689462\pi\)
−0.560684 + 0.828030i \(0.689462\pi\)
\(588\) 0 0
\(589\) −957.010 −1.62480
\(590\) 0 0
\(591\) 312.735i 0.529162i
\(592\) 0 0
\(593\) 282.430i 0.476274i 0.971232 + 0.238137i \(0.0765367\pi\)
−0.971232 + 0.238137i \(0.923463\pi\)
\(594\) 0 0
\(595\) −51.0920 + 86.2739i −0.0858688 + 0.144998i
\(596\) 0 0
\(597\) 897.739i 1.50375i
\(598\) 0 0
\(599\) 498.597i 0.832382i −0.909277 0.416191i \(-0.863365\pi\)
0.909277 0.416191i \(-0.136635\pi\)
\(600\) 0 0
\(601\) −287.496 −0.478363 −0.239182 0.970975i \(-0.576879\pi\)
−0.239182 + 0.970975i \(0.576879\pi\)
\(602\) 0 0
\(603\) 151.934 0.251964
\(604\) 0 0
\(605\) −355.662 210.625i −0.587871 0.348141i
\(606\) 0 0
\(607\) −844.260 −1.39087 −0.695437 0.718587i \(-0.744789\pi\)
−0.695437 + 0.718587i \(0.744789\pi\)
\(608\) 0 0
\(609\) −212.461 −0.348869
\(610\) 0 0
\(611\) 1066.46i 1.74543i
\(612\) 0 0
\(613\) 975.340i 1.59109i 0.605892 + 0.795547i \(0.292816\pi\)
−0.605892 + 0.795547i \(0.707184\pi\)
\(614\) 0 0
\(615\) −137.720 81.5588i −0.223935 0.132616i
\(616\) 0 0
\(617\) 319.229i 0.517389i −0.965959 0.258695i \(-0.916708\pi\)
0.965959 0.258695i \(-0.0832923\pi\)
\(618\) 0 0
\(619\) 845.837i 1.36646i 0.730205 + 0.683228i \(0.239425\pi\)
−0.730205 + 0.683228i \(0.760575\pi\)
\(620\) 0 0
\(621\) 632.190 1.01802
\(622\) 0 0
\(623\) −514.489 −0.825826
\(624\) 0 0
\(625\) −336.153 + 526.902i −0.537846 + 0.843043i
\(626\) 0 0
\(627\) −617.764 −0.985269
\(628\) 0 0
\(629\) −361.080 −0.574055
\(630\) 0 0
\(631\) 322.653i 0.511335i 0.966765 + 0.255668i \(0.0822953\pi\)
−0.966765 + 0.255668i \(0.917705\pi\)
\(632\) 0 0
\(633\) 360.087i 0.568858i
\(634\) 0 0
\(635\) −258.409 153.032i −0.406944 0.240995i
\(636\) 0 0
\(637\) 550.712i 0.864541i
\(638\) 0 0
\(639\) 100.058i 0.156585i
\(640\) 0 0
\(641\) 167.659 0.261558 0.130779 0.991412i \(-0.458252\pi\)
0.130779 + 0.991412i \(0.458252\pi\)
\(642\) 0 0
\(643\) 118.227 0.183867 0.0919335 0.995765i \(-0.470695\pi\)
0.0919335 + 0.995765i \(0.470695\pi\)
\(644\) 0 0
\(645\) 306.372 + 181.435i 0.474995 + 0.281295i
\(646\) 0 0
\(647\) 783.464 1.21092 0.605459 0.795876i \(-0.292989\pi\)
0.605459 + 0.795876i \(0.292989\pi\)
\(648\) 0 0
\(649\) −171.950 −0.264946
\(650\) 0 0
\(651\) 280.141i 0.430324i
\(652\) 0 0
\(653\) 28.4352i 0.0435455i −0.999763 0.0217727i \(-0.993069\pi\)
0.999763 0.0217727i \(-0.00693102\pi\)
\(654\) 0 0
\(655\) 285.314 481.781i 0.435593 0.735543i
\(656\) 0 0
\(657\) 52.9051i 0.0805253i
\(658\) 0 0
\(659\) 594.296i 0.901814i 0.892571 + 0.450907i \(0.148899\pi\)
−0.892571 + 0.450907i \(0.851101\pi\)
\(660\) 0 0
\(661\) 495.511 0.749638 0.374819 0.927098i \(-0.377705\pi\)
0.374819 + 0.927098i \(0.377705\pi\)
\(662\) 0 0
\(663\) 231.176 0.348682
\(664\) 0 0
\(665\) 355.340 600.028i 0.534346 0.902297i
\(666\) 0 0
\(667\) −441.599 −0.662067
\(668\) 0 0
\(669\) 257.231 0.384501
\(670\) 0 0
\(671\) 335.530i 0.500045i
\(672\) 0 0
\(673\) 168.874i 0.250927i 0.992098 + 0.125464i \(0.0400418\pi\)
−0.992098 + 0.125464i \(0.959958\pi\)
\(674\) 0 0
\(675\) −344.693 628.775i −0.510657 0.931519i
\(676\) 0 0
\(677\) 895.899i 1.32334i 0.749797 + 0.661668i \(0.230151\pi\)
−0.749797 + 0.661668i \(0.769849\pi\)
\(678\) 0 0
\(679\) 24.6745i 0.0363394i
\(680\) 0 0
\(681\) 41.3042 0.0606522
\(682\) 0 0
\(683\) −359.410 −0.526223 −0.263112 0.964765i \(-0.584749\pi\)
−0.263112 + 0.964765i \(0.584749\pi\)
\(684\) 0 0
\(685\) 108.647 183.462i 0.158609 0.267828i
\(686\) 0 0
\(687\) 396.926 0.577767
\(688\) 0 0
\(689\) −637.680 −0.925516
\(690\) 0 0
\(691\) 515.701i 0.746311i 0.927769 + 0.373155i \(0.121724\pi\)
−0.927769 + 0.373155i \(0.878276\pi\)
\(692\) 0 0
\(693\) 33.6857i 0.0486085i
\(694\) 0 0
\(695\) −566.454 + 956.514i −0.815041 + 1.37628i
\(696\) 0 0
\(697\) 60.5360i 0.0868523i
\(698\) 0 0
\(699\) 348.510i 0.498584i
\(700\) 0 0
\(701\) 1370.37 1.95488 0.977438 0.211221i \(-0.0677441\pi\)
0.977438 + 0.211221i \(0.0677441\pi\)
\(702\) 0 0
\(703\) 2511.28 3.57224
\(704\) 0 0
\(705\) −784.293 464.463i −1.11247 0.658813i
\(706\) 0 0
\(707\) 468.018 0.661978
\(708\) 0 0
\(709\) 662.128 0.933890 0.466945 0.884286i \(-0.345355\pi\)
0.466945 + 0.884286i \(0.345355\pi\)
\(710\) 0 0
\(711\) 138.008i 0.194104i
\(712\) 0 0
\(713\) 582.270i 0.816649i
\(714\) 0 0
\(715\) 429.181 + 254.163i 0.600253 + 0.355473i
\(716\) 0 0
\(717\) 4.55302i 0.00635010i
\(718\) 0 0
\(719\) 370.003i 0.514608i −0.966331 0.257304i \(-0.917166\pi\)
0.966331 0.257304i \(-0.0828341\pi\)
\(720\) 0 0
\(721\) −38.3415 −0.0531782
\(722\) 0 0
\(723\) 569.964 0.788331
\(724\) 0 0
\(725\) 240.776 + 439.214i 0.332105 + 0.605812i
\(726\) 0 0
\(727\) 607.695 0.835894 0.417947 0.908471i \(-0.362750\pi\)
0.417947 + 0.908471i \(0.362750\pi\)
\(728\) 0 0
\(729\) 804.700 1.10384
\(730\) 0 0
\(731\) 134.668i 0.184224i
\(732\) 0 0
\(733\) 1066.76i 1.45533i 0.685931 + 0.727666i \(0.259395\pi\)
−0.685931 + 0.727666i \(0.740605\pi\)
\(734\) 0 0
\(735\) 405.005 + 239.847i 0.551027 + 0.326322i
\(736\) 0 0
\(737\) 665.591i 0.903108i
\(738\) 0 0
\(739\) 558.366i 0.755570i 0.925893 + 0.377785i \(0.123314\pi\)
−0.925893 + 0.377785i \(0.876686\pi\)
\(740\) 0 0
\(741\) −1607.81 −2.16978
\(742\) 0 0
\(743\) −1112.00 −1.49664 −0.748319 0.663339i \(-0.769139\pi\)
−0.748319 + 0.663339i \(0.769139\pi\)
\(744\) 0 0
\(745\) 86.4659 + 51.2056i 0.116062 + 0.0687324i
\(746\) 0 0
\(747\) −178.299 −0.238687
\(748\) 0 0
\(749\) −519.137 −0.693107
\(750\) 0 0
\(751\) 1207.34i 1.60764i 0.594873 + 0.803820i \(0.297202\pi\)
−0.594873 + 0.803820i \(0.702798\pi\)
\(752\) 0 0
\(753\) 204.158i 0.271127i
\(754\) 0 0
\(755\) −219.242 + 370.213i −0.290387 + 0.490348i
\(756\) 0 0
\(757\) 87.7776i 0.115955i 0.998318 + 0.0579773i \(0.0184651\pi\)
−0.998318 + 0.0579773i \(0.981535\pi\)
\(758\) 0 0
\(759\) 375.864i 0.495209i
\(760\) 0 0
\(761\) 67.0202 0.0880686 0.0440343 0.999030i \(-0.485979\pi\)
0.0440343 + 0.999030i \(0.485979\pi\)
\(762\) 0 0
\(763\) −108.687 −0.142447
\(764\) 0 0
\(765\) −18.7549 + 31.6695i −0.0245162 + 0.0413980i
\(766\) 0 0
\(767\) −447.522 −0.583470
\(768\) 0 0
\(769\) 342.869 0.445863 0.222932 0.974834i \(-0.428437\pi\)
0.222932 + 0.974834i \(0.428437\pi\)
\(770\) 0 0
\(771\) 756.587i 0.981306i
\(772\) 0 0
\(773\) 244.756i 0.316631i −0.987389 0.158316i \(-0.949394\pi\)
0.987389 0.158316i \(-0.0506063\pi\)
\(774\) 0 0
\(775\) 579.126 317.475i 0.747259 0.409646i
\(776\) 0 0
\(777\) 735.116i 0.946095i
\(778\) 0 0
\(779\) 421.023i 0.540466i
\(780\) 0 0
\(781\) 438.330 0.561242
\(782\) 0 0
\(783\) −574.657 −0.733917
\(784\) 0 0
\(785\) −40.8516 + 68.9821i −0.0520403 + 0.0878753i
\(786\) 0 0
\(787\) 1120.38 1.42361 0.711806 0.702376i \(-0.247877\pi\)
0.711806 + 0.702376i \(0.247877\pi\)
\(788\) 0 0
\(789\) −208.063 −0.263705
\(790\) 0 0
\(791\) 731.695i 0.925025i
\(792\) 0 0
\(793\) 873.260i 1.10121i
\(794\) 0 0
\(795\) −277.723 + 468.963i −0.349337 + 0.589891i
\(796\) 0 0
\(797\) 1344.51i 1.68696i −0.537161 0.843480i \(-0.680503\pi\)
0.537161 0.843480i \(-0.319497\pi\)
\(798\) 0 0
\(799\) 344.742i 0.431467i
\(800\) 0 0